Find the Critical Value or Values Of $\chi ^ { 2 }$

question 18

Multiple Choice

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows:
$$\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$$ where $k$ is the number of degrees of freedom and $z$ is the critical value. To find the lower critical value, the negative $z$ -value is used, to find the upper critical value, the positive $z$ -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a two-tailed hypothesis test with $\mathrm { n } = 104$ and $\alpha = 0.10$ .

• A) \(\chi ^ { 2 } \approx 84.992\) and \(\chi ^ { 2 } \approx 121.646\)
• B) \(\chi ^ { 2 } \approx 80.300\) and \(\chi ^ { 2 } \approx 127.406\)
• C) \(\chi ^ { 2 } \approx 81.186\) and \(\chi ^ { 2 } \approx 128.520\)
• D) \(\chi ^ { 2 } \approx 85.903\) and \(\chi ^ { 2 } \approx 122.735\)

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Definitions:

ADP

Adenosine diphosphate, a molecule involved in ATP synthesis, it releases energy when it is converted to ATP in cellular respiration.

Muscle Contraction

The tightening of muscle fibers initiated by electrical impulses, leading to shortening of the muscle and movement or force generation.

Sarcoplasmic Reticulum

Smooth endoplasmic reticulum of skeletal muscle cells; surrounds the myofibrils and stores calcium ions.

Calcium Ions

Electrically charged calcium atoms (Ca2+) that play a crucial role in various physiological processes, including muscle contraction, neurotransmitter release, and bone formation.